中文摘要：

Ф-混合的概念作为弱相关的衡量尺度在实际中被广泛应用，且缺失数据现象在各领域常有发生，已有文献对相依和缺失数据两种情形的统计推断分别进行了深入研究，但对同时存在相依和缺失数据情形的研究较少．本文研究既有相依又有缺失情形的统计推断，即研究Ф-混合样本下缺失数据情形线性模型回归系数的经验似然比统计量的渐近分布．我们采取回归填补方法对响应变量的缺失值进行补足，得到线性模型回归系数的“完全”样本数据．在此基础上利用记分函数构造线性模型回归系数的经验似然比统计量，在一定条件下证明经验似然比统计量渐近服从卡方分布，这一结论为构造咖混合样本下缺失数据情形线性模型回归系数的置信域提供了理论依据．

英文摘要：

The concept of Ф-mixing has been used extensively as measures of the weak depen- dence, and the phenomenon of missing data often occurs in various application fields. In existing literatures, the statistical inference under the dependence and missing data, has been deeply studied. However, there are few studies on the case of the dependent and missing data simultaneously. This paper is concerned with the statistical inference simultaneously under the dependence and missing data. In other words, this paper discusses the asymptotic distributions of empirical likelihood ratio statistics for regression coefficients in a linear model under Ф- mixing samples with missing data. The regression imputation method is applied to impute the missing data of the response variables, and thus ‘complete＇ data for regression coefficients in the linear model are obtained. Furthermore, we employ the score functions to establish the empirical likelihood ratio statistics for the regression vector in the linear model. Under some conditions, it is proved that the empirical likelihood ratio statistics are asymptotically Chi square distributed. This conclusion provides a theoretical basis for the confidence region of the regression coefficients of a linear model under Ф-mixing samples with missing datA.